I do not know if hunting rifle bullets do this or not.
I think that Abrams tank has smooth barrel.
So cannot be compared to rifle bullet ballistic.
Next is rifle bullet stabilization (in air).
When cartridge is seated in the chamber it is not perfectly aligned with barrel, as there are tolerances between cartridge and chamber as defined by SAAMI or CIP standard.
So, when fired, bullet is not perfectly aligned with barrel axis.
When bullet is exiting the barrel, axis of the spinning bullet and axis of barrel are still diverging.
Bullet has the spin and will stabilize with gyroscopic effect after certain time, end eventually will come to intended flight path.
(FYI: ships gyro compass after starting takes few hours to stabilize)
So, consequently to the industry tolerances and bullet shape imperfections, there is so called precession of bullet (rotation around the center of mass) and there is so called nutation, a circular movement around bullet tip.
Both phenomena decrease (reduce) with the distance travelled from the barrel.
Longer the distance, less of those two effects. (this means the bullet stabilize with distance)
This is the reason why high end match barrels and custom ammunition have generally smaller tolerances, ammunition for them is custom made (reloaded), all this in order to improve intrinsic accuracy, but the drawback is that not all factory standard ammunition can fit the chamber.
Next is terminal ballistic.
I dont think that there is any correlation between external and terminal ballistic, or stability of bullet in flight with penetration or tumbling, or stability in body tissue. This can be seen in various gelatin tests, or shooting in the water.
Some bullets penetrate better, some are tumbling. Meplats and round nose solids are known to be most stable penetrators.
Bullet factories test their products till they get what they want to get, in terms of terminal ballistic.
There is a lot of trial and error in entire process of testing when designing a bullet.
But general accumulated knowledge with these tests historically has increased significantly, so they pretty much have an idea in advance how new design will perform.
There is only one case that I remember reading somewhere is that same bullets', of expanding type, will have better terminal effect on animal - with faster twist.
I think this is because they cut the permanent wound channel with faster rate, and thus in theory could cause more bleeding on animal - with more rotations within penetration path.
(If CNS is not hit, then bleeding is primary cause of death in animal shot).
Scheme from internet (distance increase to the left):